Bifurcation analysis of a smoothed model of a forced impacting beam and comparison with an experiment

A piecewise-linear model with a single degree of freedom is derived from first principles for a driven vertical cantilever beam with a localized mass and symmetric stops. The resulting piecewise-linear dynamical system is smoothed by a switching function (nonlinear homotopy). For the chosen smoothin...

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Bibliographic Details
Published in:arXiv.org 2013-08
Main Authors: Elmegård, M, Krauskopf, B, Osinga, H M, Starke, J, Thomsen, J J
Format: Article
Language:English
Subjects:
Bifurcations
Cantilever beams
First principles
Mathematical models
Orbits
Parameters
Smoothing
Switching
Online Access:Get full text
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Summary:A piecewise-linear model with a single degree of freedom is derived from first principles for a driven vertical cantilever beam with a localized mass and symmetric stops. The resulting piecewise-linear dynamical system is smoothed by a switching function (nonlinear homotopy). For the chosen smoothing function it is shown that the smoothing can induce bifurcations in certain parameter regimes. These induced bifurcations disappear when the transition of the switching is sufficiently and increasingly localized as the impact becomes harder. The bifurcation structure of the impact oscillator response is investigated via the one- and two-parameter continuation of periodic orbits in the driving frequency and/or forcing amplitude. The results are in good agreement with experimental measurements.
ISSN:2331-8422